Rough set method

The rough set concept is a mathematical approach to deal with data imprecision, fuzziness, vagueness, and uncertainty. The theory of rough sets is complex mathematically and often considered to be too obscure for widespread implementation in engineering applications. The purpose of this section is to present rough sets as a MOO method that can be easily understood and implemented. The objective of RSM is to assess 

A handful of solutions, usually 3 to 7, from different regions of the Pareto domain are selected and presented to a decision-maker who has an intimate knowledge of the process being optimized. The decision-maker is given the task of ordering the small set of solutions from the most preferred to the least preferred. This ranking procedure captures and encapsulates the expert s knowledge of the process, which RSM will use to rank all solutions in the Pareto domain. 

The next step is to establish a set of rules that are based on the expert s ranked set and ranges of indifference. Here, each solution in the ranked set is compared to every other solution in order to define rules of preference (P rules) and rules of non-preference (NP rules). A mle takes the form of a set of values, one for each criterion, where each value may be either 1 or 0. A value of 1 indicates that the first solution is better than the second with respect to that criterion, while a value of 0 indicates that the first solution is worse than, or not significantly different from, the second with respect to that criterion. If it is desired to include the threshold of indifference in the elaboration of the rules, ranking the second solution in the comparison is always considered in the worst possible light by adding or subtracting the range of indifference, as appropriate, to it. In other words, the first solution in the comparison is 

When the entire set of P and NP rules has been established, some rules need to be eliminated for two reasons. First, if two P rules are the same, or if two NP rules are the same, then the rule needs to be included only once since it represents only one type of preference. Second, if a P rule is identical to a NP rule, they are both eliminated since the expert cannot rank one solution better than another solution for the same reason that he considers a solution worse than another solution. 

RSM is able to capture the knowledge that the decision-maker has of his/her process in a very straightforward manner. However, the main limitation of RSM is its reliance on the decision-maker s ranking of a very small set of solutions selected from the Pareto domain. Some of the issues associated with the generation of ranking rules and the subsequent ranking process are summarized below. 

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Keywords Net flow method, rough set method, thresholds, concordance index, discordance index, preference and non-preference rules, ranking, gluconic acid production. 

Specifically, rest of this chapter begins by very briefly considering MOO in general, followed by a more detailed discussion of the algorithm of net flow and rough set methods, whilst illustrating these with simple examples. The last section of the chapter is devoted to the application of this method to the production of gluconic acid. 

Renaud, J., Thibault, J., Lanouette, R., Kiss, L.N., Zaras, K., and Eonteix, C. (2007). Comparison of two multicriteria methods Net Elow and Rough Set methods for aid to decision in a high yield pulping process. European J. Oper. Research, 177 1418-1432. 

Vafaeyan, S., Thibault, J., and Titica, M. (2007). Multi-criteria optimization of beer quality using rough set method. IF AC 10 Conference on Computer Applications in Biotechnology, Cancun, Mexico, 4-6 June. 

Chevre, N., Gagne, F., Gagnon, P. and Blaise, C. (2003b) Application of rough sets analysis to identify polluted aquatic sites based on a battery of biomarkers a comparison with classical methods. Chemosphere, 51, 13-23. 

Net Flow and Rough Sets Two Methods for Ranking the Pareto Domain 191... 

Bao Xin-Zhong, Zhang Jian-Bin, Liu Cheng, 2009. A New Method of Ascertaining Attribute Weight Based on Rough Sets Conditional Information Entropy. Chinese Journal of Management Science, 6(3) 131-135. 

Sun Bin, Wang Li-Jie, 2006. Study of the Method for Determining Weight Based on Rough Set Theory. Computer Engineering and Applications, 29 216-217. 

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